1-dim Penrose tiling = "musical sequence"? Why?

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SUMMARY

The discussion centers on the concept of "musical sequences" in one-dimensional Penrose tiling, as referenced in Martin Gardner's work and linked to John Horton Conway. The term "musical sequence" is derived from the aperiodic intervals that resemble musical patterns, although the connection to music remains unclear. The conversation highlights the use of Amman bars for generating aperiodic tilings and explores the historical context of the terminology. Ultimately, the analogy between musical sequences and song forms is suggested, but definitive reasoning from Conway is lacking.

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  • Understanding of Penrose tiling and its properties
  • Familiarity with aperiodic sequences and their mathematical implications
  • Knowledge of musical theory, particularly regarding interval patterns
  • Access to academic resources on Conway's work and related mathematical literature
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  • Research "Conway's Game of Life" and its implications in mathematical patterns
  • Explore "Ammann bars" and their role in aperiodic tiling generation
  • Study "Fibonacci sequences" in both mathematics and music theory contexts
  • Investigate the relationship between aperiodicity in music and mathematics
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Mathematicians, music theorists, and anyone interested in the intersection of mathematical concepts and musical structures will benefit from this discussion.

nomadreid
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In several places (e.g., page 12 of http://www.cs.williams.edu/~bailey/06le.pdf), I have come across the aperiodic intervals in a one-dimensional Penrose tiling as "musical sequences". I do not see the connection between aperiodicity and music.
The history of a fruitless but amusing search:
(a) The best I could find is that the timbre of a hoarse voice, such as whispering, uses aperiodicity vibrations of the vocal chords, (but that doesn't help.)
(b) Amusingly enough, when I used included the key words "Amman bars", which can be used to generate the 1-d aperiodic tilings, Google gives me primarily sites about pubs in the capital of Jordan.
(c) Martin Gardner (https://www.maa.org/sites/default/files/pdf/pubs/focus/Gardner_PenroseTilings1-1977.pdf) says that Conway invented the name "musical sequence" in this context, but Gardner just labels them "Fibonacci sequences". Then, a search for Conway and Fibonacci Sequences turns up the fact that there is a classical music ensemble called "Fibonacci Sequences" which gave a concert in Conway Hall in London.
So, does anyone know why the name "musical sequence" is appropriate here?
 
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Thanks, Asymptotic. They do define what is meant by musical sequence "The spacing between bars is either long or short. In these musical sequences a short cannot follow a short and a long cannot follow two longs." and "In musical sequences a long interval can follow another long interval but a short interval must follow two long intervals, and a short interval must be followed by a long one." However, I still do not see what this has to do with music.
 
I'm thinking the analogy is to song forms. For example, AAA is common in traditional folk (think "House of the Rising Sun") where the same figure is repeated ad infinitum, AABA is perhaps the most prevalent (here is a good run down on AABA), while other forms include AABB, ABAB, and so on, sometimes interspersed with C, D, or more discrete sections.
 
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Thanks, Asymptotic. That is as good a guess as I suppose is possible without a definitive answer from Conway (John Horton) himself. He's 80 now, and trying to get an answer from him would probably not be a Good Thing. Unfortunately, as I do not have access to a decent academic library (for access, for example, to the three books of Conway's that Gardner cites) and the Internet comes up with nothing (unless I wanted to order all those books), I will have to assume that Conway's love of music made him stretch an analogy a bit far. Or maybe this is what music looks like for the "creatures" from Conway's Game of Life.
 
They're well described in Grünbaum and Shephard's book Tilings and Patterns (chapter 10, section about Ammann bars in Penrose tilings). They say Conway chose this name, like he chose the names of the vertex configurations like Jack, Queen and King... so I guess it's basically about fun and games :)